Abstract: We study a relaxation scheme of the Jin and Xin type for conservation laws with a flux function that depends discontinuously on the spatial location through a coefficient . If , we show that the relaxation scheme produces a sequence of approximate solutions that converge to a weak solution. The Murat-Tartar compensated compactness method is used to establish convergence. We present numerical experiments with the relaxation scheme, and comparisons are made with a front tracking scheme based on an exact Riemann solver.

18.
J. M.-K. Hong. Part I: An extension of the Riemann problems and Glimm's method to general systems of conservation laws with source terms. Part II: A total variation bound on the conserved quantities for a generic resonant nonlinear balance laws. PhD thesis, University of California, Davis, 2000.

J. M.-K. Hong. Part I: An extension of the Riemann problems and Glimm's method to general systems of conservation laws with source terms. Part II: A total variation bound on the conserved quantities for a generic resonant nonlinear balance laws. PhD thesis, University of California, Davis, 2000.